Solute-and-dumbbell defect diffusion in b.c.c. lattices

Abstract

Defect and solute diffusion coefficients, namely D _I and D _B∗, are calculated for a b.c.c. lattice when diffusion occurs by a dumbbell mechanism. Two possible symmetries of the defect are envisaged, together with all the jump frequencies invoked so far to interpret the experimental data. For simplicity and tractability, only the binding energy of the mixed dumbbell is taken into account; all the interaction energies of a solute-defect complex when separated by a first-neighbour distance or more are ignored. The full correlation effect of the infinite lattice is taken into account using a double Fourier-Laplace transform. Unlike the vacancy case, the defect concentration C _I does not enter D _B∗ in a simple multiplicative way; the self-diffusion coefficient D _A∗ is not equal to f ₀ C _I D _I, where f ₀ is the correlation factor for self-diffusion, because the average jump length of an atom is not equal to the jump length of the defect; finally, the isotope effect is a complicated function of the jump frequencies and cannot be restated in the simple form f ₀ ΔK.